What is (21x^5-21y^5)/(3x-3y) ?

The solution to (21x^5-21y^5)/(3x-3y) is 7x^4+7x^3y+7x^2y^2+7xy^3+7y^4

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simplify (21x^5-21y^5)/(3x-3y)

simplify

\frac{21 x ^{5} - 21 y ^{5}}{3 x - 3 y}

7 x^{4} + 7 x^{3} y + 7 x^{2} y^{2} + 7 x y^{3} + 7 y^{4}

Solution steps

\frac{21 x ^{5} - 21 y ^{5}}{3 x - 3 y}

Factor

21 x^{5} - 21 y^{5} : 21 (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

= \frac{21 ( x - y ) ( x ^{4} + x ^{3} y + x ^{2} y ^{2} + x y ^{3} + y ^{4} )}{3 x - 3 y}

Factor out common term

3

= \frac{21 ( x - y ) ( x ^{4} + x ^{3} y + x ^{2} y ^{2} + x y ^{3} + y ^{4} )}{3 ( x - y )}

Cancel the common factor:

x - y

= \frac{21 ( x ^{4} + x ^{3} y + x ^{2} y ^{2} + x y ^{3} + y ^{4} )}{3}

Divide the numbers:

\frac{21}{3} = 7

= 7 (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

Distribute parentheses

= 7 x^{4} + 7 x^{3} y + 7 x^{2} y^{2} + 7 x y^{3} + 7 y^{4}

\frac{32 x ^{6} y ^{10}}{x}

\frac{- \frac{6}{7}}{( - \frac{5}{4} )}

(2 y - 3) (3 y - 2)

3 x^{2} (4 x^{3} - 2 x^{2} + 7 x - 4)

\frac{sec ( x ) csc ( x ) - tan ( x )}{sec ( x ) csc ( x )}

What is (21x^5-21y^5)/(3x-3y) ?
The solution to (21x^5-21y^5)/(3x-3y) is 7x^4+7x^3y+7x^2y^2+7xy^3+7y^4